-LRB- CNN -RRB- Andrew Brannan , 66 , who is scheduled to be put to death this week for the murder of a 22-year-old Georgia sheriff 's deputy in 1998 , is hoping his sentence will be found uniquely unconstitutional .

His defense attorneys claim Brannan , a decorated veteran who served in Vietnam in the early '70s , was suffering from post-traumatic stress and bipolar disorder at the time of the shooting and was off his medication .

In a petition filed Monday with the Butts County Superior County , Brannan 's attorneys are requesting the Brannan 's life be spared because it violates the U.S. Constitution .

The appeal states that `` executing American combat veterans whose service-related mental impairments played a role in subsequent violent conduct violates the Eighth and Fourteenth Amendments to the United States Constitution and analogous provisions of the Georgia Constitution . ''

The document goes on to say `` death is inappropriate for those with diminished capacities to understand and process information , to communicate , to abstract from mistakes and learn from experience , to engage in logical reasoning , to control impulses , and to understand the reactions of others . ''

Attorneys Joseph Loveland Jr. and Brian Kammer , who represent Brannan , say that the death penalty is reserved for the `` worst of the worst '' offenders who commit murder and that Brannan does not fit that category . They contend his mental problems were directly related to his combat service and defense of the country 's interests and ideals .

They are also petitioning the Georgia Parole Board that his sentence be commuted to life in prison .

The killing of Laurens County Deputy Kyle Dinkheller was captured on the deputy 's dash camera just outside Dublin , Georgia . Versions of the video have been uploaded to YouTube .

Brannan is seen in the video confronting Dinkheller after being pulled over for driving almost 100 miles per hour in his pickup .

Brannan appears to be confrontational from the start , acting irrational as the deputy tells him to keep his hands out of his pocket . He then mocks the deputy and at one point seems to dance around yelling `` shoot me '' at Dinkheller . Brannan then yells that he is a Vietnam veteran . He lunges at the deputy before he runs back to his truck , grabs a rifle and begins to shoot .

The video goes on to show a heated gun battle as both men hide behind their vehicles for cover . Bullets appear to pierce the windshield of the deputy 's car . Brannan 's car door window shatters above his head .

Dinkheller and Brannan are shot and wounded in the battle . But Brannan is able to advance on the deputy , and off camera , you hear the deputy scream before Brannan repeatedly shoots Dinkheller and then flees the scene . Dinkheller died , leaving behind a wife and child .

Brannan , who had no criminal record before the shooting , was convicted of the murder in 2000 .

During the trial , Kammer says the defense did present evidence that Brannan suffered from PTSD but claims that crucial testimony from the VA doctor treating him was never heard .

His sentence was appealed , and a judge ordered a new sentencing trial , but that was later overturned by the Georgia Supreme Court .

Kyle Dinkheller 's father , Kirk Dinkheller , posted on his Facebook page earlier this month that `` January 12 , 2015 it will be 17 years since my son Kyle was murdered in the line of duty and on January 13 , 2015 his killer will finally be held accountable . Nothing will ever bring my son back , but finally some justice for the one who took him from his children and his family . ''

Brannan is scheduled to die of lethal injection at 7 p.m. ET Tuesday .

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Defense attorneys claim Andrew Brannan was suffering from post-traumatic stress and bipolar disorder

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Brannan is scheduled to be executed at 7 p.m. ET Tuesday in Georgia

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He killed Deputy Kyle Dinkheller , 22 , in 1998 ; YouTube videos show the deadly confrontation